Question

What is the mass of \(6.4 \times 10^{22}\) molecules of \(\mathrm{SO}_{2} ?\)

Short answer

The mass of \(6.4 \times 10^{22}\) molecules of \(\mathrm{SO}_{2}\) is approximately 68.02 g.

Step-by-step solution

Calculate the number of moles

The number of moles can be calculated using the formula: n = N/NA, where N is the number of molecules (given as \(6.4 \times 10^{22}\)) and NA is the Avogadro’s number (\(6.022 \times 10^{23} \, \mathrm{mol}^{-1}\)). Hence, n = \(6.4 \times 10^{22} / 6.022 \times 10^{23} = 1.062 \, \mathrm{mol}\) (rounded).

Calculate the molar mass of \(\mathrm{SO}_{2}\)

The molar mass of \(\mathrm{SO}_{2}\) can be calculated by adding up the molar masses of the individual atoms in a molecule of \(\mathrm{SO}_{2}\) i.e., Sulphur (S) and Oxygen (O). Molar mass of S is 32.06 g/mol and that of O is 16.00 g/mol. Hence, molar mass of \(\mathrm{SO}_{2} = 32.06 \, \mathrm{g/mol} + 2 \times 16.00 \, \mathrm{g/mol} = 64.06 \, \mathrm{g/mol}\)

Find the mass using the moles and the molar mass

The mass of \(\mathrm{SO}_{2}\) can be calculated using the formula: mass = n × molar mass, where n is the number of moles calculated in step 1 and molar mass is the molar mass calculated in step 2. Hence, mass = \(1.062 \, \mathrm{mol} \times 64.06 \, \mathrm{g/mol} = 68.02 \, \mathrm{g}\) (rounded).

Key concepts

Avogadro's Number

Avogadro's number is a fundamental concept in chemistry used to define the exact number of particles, such as atoms or molecules, present in one mole of a substance. This number is fixed at approximately \(6.022 \times 10^{23}\), which means that one mole of any element or compound contains exactly this many particles. This large number helps chemists convert between the atomic scale and the scale usable in the laboratory.

• Universal constant: Avogadro's number is a constant that applies to all substances.
• Conversion tool: It enables the conversion of atomic-scale measurements to more manageable numbers.
• Support for calculations: It is essential for calculating the number of moles from a given quantity of particles.

For example, if we need to calculate the number of moles from \(6.4 \times 10^{22}\) molecules of \(\mathrm{SO}_{2}\), we use Avogadro's number by dividing the given molecules by \(6.022 \times 10^{23}\). This operation tells us that we have about \(1.062\) moles of \(\mathrm{SO}_{2}\).

Number of Moles

The number of moles is a measure used to express amounts of a chemical substance, making it easier to work with the macroscopic amounts that chemists use in the laboratory. Calculating moles involves relating two quantities: the number of particles in a given substance and Avogadro's number.

• What are moles: Moles represent a bridge between the atomic or molecular scale and the scale of quantity used in labs.
• Calculation method: To find the number of moles, we use the formula \(n = \frac{N}{N_{A}}\), where \(n\) is the number of moles, \(N\) is the number of molecules, and \(N_{A}\) is Avogadro's number.
• Practical example: In the given problem, \(n = \frac{6.4 \times 10^{22}}{6.022 \times 10^{23}} = 1.062\) moles.

In practice, knowing the number of moles helps chemists accurately measure out substances for reactions, ensuring correct proportions and results.

Molecule-to-Mass Conversion

Converting from a number of molecules to a mass is a key skill in chemistry, allowing chemists to measure how much of a substance is needed for a reaction or present in a sample. This conversion requires calculating the number of moles first, and then using the substance's molar mass.

• From molecules to moles: Start by calculating the number of moles using Avogadro’s number, as we've done already.
• Using molar mass: Next, apply the molar mass, which is the mass of one mole of the substance, such as \(64.06\, \mathrm{g/mol}\) for \(\mathrm{SO}_{2}\).
• Final mass calculation: Multiply the number of moles by the molar mass to find the total mass, e.g., the mass of \(\mathrm{SO}_{2}\) is \(1.062\, \mathrm{mol} \times 64.06\, \mathrm{g/mol} = 68.02\, \mathrm{g}\).

This process gives a practical amount of a substance that can be measured and used, linking the microscopic world of molecules to tangible quantities. It is essential for various laboratory work, industrial processes, and scientific research.